Equationsis

Equationsis is an emerging interdisciplinary field that studies equations as mathematical objects and as vehicles for representing and analyzing real-world relationships. Proponents describe it as a framework for understanding how equations are formed, transformed, and interpreted across disciplines, from physics and engineering to economics and social sciences. The focus is not on solving individual equations alone, but on the structural properties and epistemic role of equations within models.

Origin and terminology: The name "equationsis" combines Latin "equatio" for equation with the suffix "-sis", signaling a systematic study. Although not universally adopted, the term appears in theoretical discussions and in some experimental curricula exploring the philosophy of modelling.

Key concepts: Representational equivalence, invariance under transformations, and the classification of equation systems by type (linear, nonlinear, differential, functional). Methods include algebraic analysis, symbolic computation, model theory, and history of science approaches to trace how scientists choose forms of equations.

Applications: In scientific modelling, equationsis informs model selection, identifiability, and interpretability by examining how changes to equation form affect conclusions. In education, it investigates how learners perceive the structure and meaning of equations. It also intersects with computer science in symbolic manipulation and programmatic reasoning about equations.

Status and criticism: Equationsis is largely theoretical and not yet standardized; it shares boundaries with philosophy of mathematics and applied mathematics. Some scholars view it as a lens for critical analysis of modelling practice, while others caution against overgeneralization of equation-centric viewpoints. See also: differential equations, philosophy of mathematics, modelling.